Self referencing userdata and garbage collection

Because my userdata objects reference themselves, I need to delete and nil a variable for the garbage collector to work.

Lua code:

obj = object:new()
-- 
-- Some time later
obj:delete()  -- Removes the self reference
obj = nil     -- Ready for collection

C Code:

typedef struct {
    int self; // Reference to the object
    int callback; // Reference to a Lua function
    // Other members and function references removed
} Object;

// Called from Lua to create a new object
static int object_new( lua_State *L ) {
    Object *obj = lua_newuserdata( L, sizeof( Object ) );

    // Create the 'self' reference, userdata is on the stack top
    obj->self = luaL_ref( L, LUA_REGISTRYINDEX );

    // Put the userdata back on the stack before returning
    lua_rawgeti( L, LUA_REGISTRYINDEX, obj->self );

    // The object pointer is also stored outside of Lua for processing in C

    return 1;
}

// Called by Lua to delete an object
static int object_delete( lua_State *L ) {
    Object *obj = lua_touserdata( L, 1 );

    // Remove the objects self reference
    luaL_unref( L, LUA_REGISTRYINDEX, obj->self );

    return 0;
}

// Called from Lua to set a callback function
static int object_set_callback( lua_State *L ) {
    Object *obj = lua_touserdata( L, 1 );

    // Unref an existing callbacks
    if ( obj->callback != 0 ) {
        luaL_unref( L, LUA_REGISTRYINDEX, obj->callback );
        obj->callback = 0;
    }

    // Set the new callback - function is on top of the stack
    obj->callback = luaL_ref( L, LUA_REGISTRYINDEX );
}

// Called from C to call a Lua function for the obj
static void do_callback( Object *obj ) {
    // Push the Lua function onto the stack
    lua_rawgeti( L, LUA_REGISTRYINDEX, obj->callback );

    // Push the userdata onto the stack
    lua_rawgeti( L, LUA_REGISTRYINDEX, obj->self );

    // Call the function
    lua_call( L, 1, 0 );
}

Is there some way I can set the object to nil in Lua, and have the delete() method called automatically? Alternatively, can the delete method nil all variables that reference the object? Can the self reference be made 'weak'?

EDIT 1: I've included code to show why the object references itself; see the do_开发者_运维百科callback function. Each object is part of a tree-like structure, with the bulk of the processing done in C, but a user can set a custom Lua function that is called under certain conditions.

EDIT 2: Another possible solution comes to mind; Instead of each obj keeping a reference to itself, can I lookup the object in the global index when I need to pass it to Lua, using its address as a key?

You could try creating a weak table in the registry and store your references there, that way setting all references of your object to nil should make it available for the gc.